In this talk, i shall provide some optimal PIR bounds, which confirmed a conjecture on optimal RIP bound. Furtheremore, i shall also investigate some results on signals recovery with redundant dictionaries, which are also related to statistics and sparse representation.

In this talk we focus on classification problems where noisy sensor
measurements collected over a time window must be classified into one or
more categories. For example, mobile phone health and insurance apps
take as input time series from the accelerometer, gyroscope and GPS
radio of the phone and output predictions as to whether the user is
still, walking, running, biking, driving etc. Standard approaches to
this problem consist of first engineering features from statistics of
the data (or a transform) over a window and then training a
discriminative classifier. For two applications we show how these
features can instead be learned in an end-to-end modeling framework with
the advantages of increased accuracy and decreased modeling and
training time. The first application is reconstructing unobserved neural connections from Calcium fluorescence time series and we introduce a novel convolutional neural network architecture
with an inverse covariance layer to solve the problem. The second
application is driving detection on mobile phones with applications to
car telematics and insurance.

In this talk we discuss how to find probabilities of extreme events in stochastic differential equations. One approach to calculation would be to perform a large number of simulations and gather statistics, but an efficient alternative is to minimize Freidlin-Wentzell action. As a consequence of the analysis one also determines the most likely trajectory that gave rise to the extreme event. We apply this approach to stochastic systems whose deterministic behavior exhibit chaos (Lorenz and Kuramoto-Sivashinsky equations), comment on the observed behavior, and discuss.

The properties of euclidean space seem natural and obvious to us, to thepoint that it took mathematicians over two thousand years to see analternative to Euclid’s parallel postulate. The eventual discovery ofhyperbolic geometry in the 19th century shook our assumptions, revealingjust how strongly our native experience of the world blinded us fromconsistent alternatives, even in a field that many see as purelytheoretical. Non-euclidean spaces are still seen as unintuitive and exotic,but with direct immersive experiences we can get a better intuitive feel forthem. The latest wave of virtual reality hardware, in particular the HTCVive, tracks both the orientation and the position of the headset within aroom-sized volume, allowing for such an experience. We use this nacenttechnology to explore the three-dimensional geometries of theThurston/Perelman geometrization theorem. This talk focuses on oursimulations of H³ and H²×E.

This talk addresses an important problem in arctic engineering due to interesting dynamic phenomena in a forced linear system. The nonautonomous system considered is representative of a whole class of engineering problems that are not approachable by standard techniques from dynamical system theory.The background are ice-induced vibrations of structures (e.g. wind turbines or measurement masts) in regions with active sea ice. Ice is a complex material and the mechanism for ice-induced vibrations is not fully clear at present. In particular, the conditions under which the observed, qualitatively different vibration regimes are active cannot be predicted accurately so far. A recent mathematical model developed by Delft University of Technology assumes that a number of parallel ice strips are pushing with a constant velocity against a flexible structure. The structure is modelled as a single degree of freedom harmonic oscillator. The contact force acts on the structure, but at the same time slows down the advancement of the ice, thereby introducing a dynamic nonlinearity in the otherwise linear system. When the local contact force becomes large enough, the ice crushes and the corresponding strip is reset to a random offset in front of the structure.This is the first mathematical model that exhibits all three different dynamic regimes that are observed in reality: for slow ice velocities the structure undergoes quasi-static sawtooth responses where all ice strips fail at the same time (a kind of synchronization phenomenon), for large ice velocities the structure response appears random, and for intermediate ice velocities the system exhibits vibrations at the structure eigenfrequency, commonly called frequency lock-in behavior. The latter type of vibrations causes a lot of damage to the structure and poses a safety and economic risk, so its occurrence needs to be predicted accurately.As I will show in this talk, the descriptive terms for the three vibration regimes are slightly misleading, as the mechanisms behind the observed behaviors are somewhat different than intuition suggests. I will present first results in analyzing the system and offer some explanations of the observed behaviors, as well as some simple criteria for the switch between the different vibration regimes.

In
this talk I will present my recent result about the ergodic properties
of nonequilibrium steady-state (NESS) for a stochastic energy exchange
model. The energy exchange model is numerically reduced from a
billiards-like deterministic particle system that models the microscopic
heat conduction in a 1D chain. By using a technique called the induced
chain method, I proved the existence, uniqueness, polynomial speed of
convergence to the NESS, and polynomial speed of mixing for the
stochastic energy exchange model. All of these are consistent with the
numerical simulation results of the original deterministic
billiards-like system.

Two-photon photoacoustic tomography (TP-PAT) is a non-invasive optical molecular imaging modality that aims at inferring two-photon absorption property of heterogeneous media from photoacoustic measurements. In this work, we analyze an inverse problem in quantitative TP-PAT where we intend to reconstruct optical coefficients in a semilinear elliptic PDE, the mathematical model for the propagation of near infra-red photons in tissue-like optical media, from the internal absorbed energy data. We derive uniqueness and stability results on the reconstructions of single and multiple coefficients, and perform numerical simulations based on synthetic data to validate the theoretical analysis.

For many problems in science and engineering, one needs to quantitatively compare shapes of objects in images, e.g., anatomical structures in medical images, detected objects in images of natural scenes. One might have large databases of such shapes, and may want to cluster, classify or compare such elements. To be able to perform such analyses, one needs the notion of shape distance quantifying dissimilarity of such entities. In this work, we focus on the elastic shape distance of Srivastava et al. [PAMI, 2011] for closed planar curves. This provides a flexible and intuitive geodesic distance measure between curve shapes in an appropriate shape space, invariant to translation, scaling, rotation and reparametrization. Computing this distance, however, is computationally expensive. The original algorithm proposed by Srivastava et al. using dynamic programming runs in cubic time with respect to the number of nodes per curve. In this work, we propose a new fast hybrid iterative algorithm to compute the elastic shape distance between shapes of closed planar curves. The asymptotic time complexity of our iterative algorithm is O(N log(N)) per iteration. However, in our experiments, we have observed almost a linear trend in the total running times depending on the type of curve data.

The Georgia Scientific Computing Symposium (GSCS) is a forum for
professors, postdocs, graduate students and other researchers in Georgia
to meet in an informal setting, to exchange ideas, and to highlight
local scientific computing research. The symposium has been held every
year since 2009 and is open to the entire research community.
The format of the day-long symposium is a set of invited
presentations, poster sessions and a poster blitz, and plenty of time to
network with other attendees. More information at http://euler.math.uga.edu/cms/GSCS-2017